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Mathematics > Analysis of PDEs

arXiv:1804.06560 (math)
[Submitted on 18 Apr 2018 (v1), last revised 18 Feb 2020 (this version, v3)]

Title:Propagation of regularity and long time behavior of $3D$ massive relativistic transport equation I: Vlasov-Nordström system

Authors:Xuecheng Wang
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Abstract:In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable for general Vlasov-Wave type coupled systems. By combining the strength of Klainerman vector field method and Fourier method, we prove global regularity and scattering for the $3D$ massive relativistic Vlasov-Nordström system for small initial data without any compact support assumption, which is widely used in the literature for the study of Vlasov solution.
Comments: Reorganized to improve presentation
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.06560 [math.AP]
  (or arXiv:1804.06560v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.06560

Submission history

From: Xuecheng Wang [view email]
[v1] Wed, 18 Apr 2018 05:28:48 UTC (57 KB)
[v2] Mon, 28 May 2018 09:34:59 UTC (60 KB)
[v3] Tue, 18 Feb 2020 08:33:22 UTC (59 KB)
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